m的三次方加3m的二次方加3m加2=0求m加1的和的2007次方加m加1的和的2008次方加m加1的和的2009次方的

m³ +3m² +3m + 2 = 0
m³ +2m² + m² +2m+ m+ 1 + 1 = 0
m(m² +2m +1) +(m² +2m +1) +1 = 0
m(m+1)² +（m+1）² +1 = 0
（m+1）²（m+1）+1 = 0
(m+1)³ = -1
所以 m+1 = - 1, m = -2 并将其代入下式
（m+1）^2007 + (m+1)^2008 + (m+1)^2009
= (-1)^2007+(-1)^2008+(-1)^2009
= -1 +1 -1
= -1